Application of the three-dimensional telegraph equation to cosmic-ray transport

Abstract

An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the Klein-Gordon equation, the telegraph equation can be solved in closed form. Illustrative examples are used to discuss the qualitative differences to the diffusion solution. The comparison with a numerical test-particle simulation reveals that some features of an intensity profile can be better explained using the telegraph approach.

arXiv comment13 pages, 6 figures, accepted for publication in "Research in Astronomy and Astrophysics"

References in corpus (5)

• Energetic particle cross-field propagation early in a solar event
• The Diffusion Approximation vs. the Telegraph Equation for Modeling Solar Energetic Particle Transport with Adiabatic Focusing. I. Isotropic Pitch-angle Scattering
• On numerical turbulence generation for test-particle simulations
• Cosmic Ray Transport with Magnetic Focusing and the "Telegraph" model
• Monte-Carlo simulations of intensity profiles for energetic particle propagation

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• Leptonic and hadronic models of high-energy nebula around V4641 Sgr
• Efficient charged particle propagation methods
• Cosmic-ray transport in blazars: diffusive or ballistic propagation?
• Stochastic dynamics from maximum entropy in action space